colour.algebra.smooth

colour.algebra.smooth(x: ArrayLike, a: ArrayLike = 0, b: ArrayLike = 1, clip: bool = False) → NDArrayFloat

Apply the smoothstep cubic Hermite interpolation function to array \(x\).

The smoothstep function creates a smooth S-shaped curve between specified edge values, commonly used for smooth transitions in colour interpolation and rendering operations.

Parameters:

• x (ArrayLike) – Input array \(x\) containing values to be transformed.

• a (ArrayLike) – Lower edge value for the interpolation domain.

• b (ArrayLike) – Upper edge value for the interpolation domain.

• clip (bool) – Whether to normalize and constrain input values to the domain [\(a\), \(b\)] before applying the smoothstep function.

Returns:

Transformed array with values smoothly interpolated using the cubic Hermite polynomial \(3x^2 - 2x^3\).

Return type:

numpy.ndarray

Examples

>>> x = np.linspace(-2, 2, 5)
>>> smoothstep_function(x, -2, 2, clip=True)
array([ 0.     ,  0.15625,  0.5    ,  0.84375,  1.     ])